Someone is waiting for the person they love to notice them. The speaker wishes that one day he will turn to her, realise something has been missing from his life, and understand that the two of them belong together. Nothing about the wish is grand. She imagines him saying her name with a smile, looking at her with joy, giving her a quick kiss and putting an arm around her.
The mood is tender but sad. Because everything is framed as "I wish," we sense that none of it is happening now, and that she may feel overlooked or unsure he will ever see her this way. The repetition of "I wish a day" and the broken ending, "I wish for day / I wish," make the voice sound halting, almost as if she trails off from hope into quiet ache. The simple, unpolished wording adds to the feeling of a private, honest confession rather than a carefully decorated one.